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\usepackage{ctex} % 中文支持
\usepackage{amsmath, amsthm, amssymb, bm} % 数学公式与符号
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\usepackage{booktabs} % 用于高质量表格
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% 信息设置
\title[一阶偏微分方程]{《常微分方程》第十一章：一阶偏微分方程}
\author[]{LQW}
%\institute[XX大学]{XX大学\quad 数学与统计学院\quad 数学与应用数学专业}
%\date{2025年6月}

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\begin{document}

% 封面页
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  \titlepage
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% 目录页
%\begin{frame}{目录}
%  \tableofcontents
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%\maketitle

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\begin{frame}{目录}

\begin{enumerate}
\item[11.1.] 一阶齐次线性偏微分方程  
\item[11.2.] 一阶拟线性偏微分方程
\item[11.3.] 几何解释

\end{enumerate}

\end{frame}

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\begin{frame}{11.1.1.  }

\begin{itemize}
\setlength{\itemsep}{0.3cm}
\item  问：求解一阶线性偏微分方程
\begin{eqnarray*}
(x+y)\frac{\partial f}{\partial x} - (x-y)\frac{\partial f}{\partial y} = 0. 
\end{eqnarray*}

\item  答：


\end{itemize}

\end{frame}

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\begin{frame}{11.1.2.  }

\begin{itemize}
\setlength{\itemsep}{0.3cm}
\item  问：求解一阶线性偏微分方程
\begin{eqnarray*}
\left\{\begin{array}{rcl}
\sqrt{x}\frac{\partial f}{\partial x} + \sqrt{y}\frac{\partial f}{\partial y} +z\frac{\partial f}{\partial z} &=& 0. \\ 
f(x,y,1) &=& xy. 
\end{array}\right.
\end{eqnarray*}

\item  答：


\end{itemize}

\end{frame}

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\begin{frame}{11.2.1. 一阶拟线性偏微分方程 }

\begin{itemize}
\setlength{\itemsep}{0.3cm}
\item  问：求解一阶线性偏微分方程
\begin{eqnarray*}
\left\{\begin{array}{rcl}
\sqrt{x}\frac{\partial f}{\partial x} + \sqrt{y}\frac{\partial f}{\partial y} &=& f(x,y). \\ 
f(1,y) &=& \sin(2y). 
\end{array}\right.
\end{eqnarray*}

\item  答：


\end{itemize}

\end{frame}

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\begin{frame}{11.3.1. 几何解释 }

\begin{itemize}
\setlength{\itemsep}{0.3cm}
\item  问：求偏微分方程 $x\frac{\partial z}{\partial x} - y\frac{\partial z}{\partial y} = z$ 的积分曲面，
使得它通过初始曲线 $$x=t, y=3t, z=1+t^2,$$ 这里 $t>0$ 为参数。

\item  答：


\end{itemize}

\end{frame}

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\end{document}
